A semi-analytical approach to characterize the relative motion in the vicinity of phobos

Davide Conte, David B. Spencer

Research output: Chapter in Book/Report/Conference proceedingConference contribution


This paper discusses a semi-analytical approach that can be used to approximate the relative motion of spacecraft around nominal periodic Distant Retrograde Orbits (DROs) in the vicinity of Mars’ largest moon, Phobos. Numerical analysis reveals that in the Circular Restricted Three-Body Problem (CR3BP) rotating reference frame, Mars-Phobos DROs can be represented analytically in a moderately accurate way by two terms of their Fourier series representations due to the fact that the mass of Phobos is much smaller than the mass of Mars. Additionally, assuming that the relative distance between spacecraft is sufficiently small, the equations of motions can be further simplified and semi-analytically solved to obtain an accurate representation of the relative motion in the vicinity of Phobos. It is found that the equations exhibit a secular behavior, which can be accurately described by the Hill-Clohessy-Wiltshire (HCW) equations, and a short-term cyclic behavior which is attributed to the gravitational attraction of Phobos that the HCW equations cannot represent.

Original languageEnglish (US)
Title of host publicationAAS/AIAA Astrodynamics Specialist Conference, 2018
EditorsPuneet Singla, Ryan M. Weisman, Belinda G. Marchand, Brandon A. Jones
PublisherUnivelt Inc.
Number of pages17
ISBN (Print)9780877036579
StatePublished - 2018
EventAAS/AIAA Astrodynamics Specialist Conference, 2018 - Snowbird, United States
Duration: Aug 19 2018Aug 23 2018

Publication series

NameAdvances in the Astronautical Sciences
ISSN (Print)0065-3438


ConferenceAAS/AIAA Astrodynamics Specialist Conference, 2018
Country/TerritoryUnited States

All Science Journal Classification (ASJC) codes

  • Aerospace Engineering
  • Space and Planetary Science


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